Answer:
Option 2 and 3 - 3 and [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex](4x-5)^2=49[/tex]
To find : What are the possible values of x ?
Solution :
Equation [tex](4x-5)^2=49[/tex]
Taking root both side,
[tex]\sqrt{(4x-5)^2}=\sqrt{49}[/tex]
[tex](4x-5)=\pm 7[/tex]
Taking [tex]4x-5=7[/tex]
[tex]4x=7+5[/tex]
[tex]4x=12[/tex]
[tex]x=\frac{12}{4}[/tex]
[tex]x=3[/tex]
Taking [tex]4x-5=-7[/tex]
[tex]4x=-7+5[/tex]
[tex]4x=-2[/tex]
[tex]x=-\frac{2}{4}[/tex]
[tex]x=-\frac{1}{2}[/tex]
The possible values of x are 3 and [tex]-\frac{1}{2}[/tex]
Therefore, option 2 and 3 are correct.
The possible values of x are; x = 3 or x = -1/2
The given equation is; (4x – 5)². = 49
By taking the square root of both sides; we have;
4x -5 = √49
4x -5 = ±7
4x = ±7 +5
Therefore; 4x = 12 or -2
x = 3 or x = -1/2
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